The film-deposition technology has been developing rapidly in recent years and the performance of thin films, especially the widely used highly reflective (HR) coatings, has been greatly improved. However, it is difficult to determine high reflectivity (R>99.9%) of HR coatings using conventional instruments and methods such as a spectrophotometer. To measure the reflectivity approaching unity, the so-called cavity ring-down (CRD) technique has been employed. It is based on the measurement of the decay time of laser power in an optical ring-down cavity, which comprises two highly reflective mirrors. The decay time is inversely proportional to the total losses of the optical ring-down cavity and directly proportional to the length of the cavity. Due to the natural characteristics of time measurement, CRD technique has the advantage of being insensitive to the power fluctuation of the light source, results in an improved accuracy in determining low losses or high reflectivities. Nowadays numerous articles and patents can be found in literature, providing various CRD arrangements and methods, especially in the fields of absorption spectroscopy and trace analyses. For detailed information, see for examples the articles by O'Keefe and Deacon in Rev. Sci. Instrum. 59(12): 2544-2551 (1988), Engeln et al. in Chem. Phys. Lett. 262: 105-109 (1996), Romanini et al. in Chem. Phys. Lett. 264: 316-322 (1997) and U.S. Pat. Nos. 6,839,140 and 6,466,322.
Herbelin et al. have proposed the use of an optical cavity for measuring the reflectivity of mirrors. In this technique, a continuous-wave (cw) laser beam with modulated intensity is coupled into an optical cavity which comprises mirrors with unknown reflectivity. The total cavity losses are determined from the phase shift induced in the laser signal while it passes through the optical cavity. The reflectivity of a planar mirror is determined by the change of total cavity loss introduced by inserting the planar mirror into the optical cavity. However, the use of a narrow-bandwidth laser in their apparatus causes large noise in the cavity output signal and results in a limited measurement sensitivity and accuracy.
U.S. Pat. No. 4,793,709 describes a pulsed cavity ring-down method for measuring the losses of an optical cavity. In this method the following steps are involved: (1) generating one laser pulse having a bandwidth that exceeds the free spectral range of the optical cavity; (2) directing that pulse into an optical cavity; (3) measuring the temporal signal of the intensity of the laser beam exiting the cavity. The amount of time span for this intensity to decay from a first predetermined value to a second predetermined value is measured and then the loss of the optical cavity is determined. However, a pulsed laser with a high peak power, which is often costly and with various complicated optical components, is needed to obtain sufficiently high output intensity from the ring-down cavity.
U.S. Pat. No. 4,571,085 presents a cavity ring-down method for measuring the decay time of an optical cavity by directing a cw laser beam into the cavity, switching the beam off when the amplitude of the cavity output signal reaches a predetermined threshold level, then monitoring the temporal decay of the laser beam intensity exiting the optical cavity immediately after switching off the beam, and measuring the intensity decay time with an oscilloscope. In this technique, a narrow-bandwidth laser is used as the light source. The spectrum of the laser drifts occasionally and randomly due to environmental temperature fluctuation, mechanical vibration, etc. The spectrum of the laser is occasionally in resonance with one or more eigen-modes of the ring-down cavity, results in rapid increases of the light intensities inside and exiting the ring-down cavity. One disadvantage of this technique is the low efficiency in the decay time measurement, due to the low probability of spectral resonance. In addition, in this technique, a fast optical switch, such as an acousto-optic modulator, is needed to switching the beam off the ring-down cavity.
Another method based on the decay time measurement for determining ultra-low loss of an optical cavity is disclosed by G. Rempe, R. J. Thompson, H. J. Kimble in “Measurement of ultra-low losses in an optical interferometer”, Opt. Lett., Vol. 17, No. 5, pp. 363 (Mar. 1, 1992). A cw laser is employed as the light source. A piezo-electric transducer (PZT) is employed to slowly scan the length of the optical cavity, making the laser frequency periodically in resonant with frequencies of the cavity eigen-modes. The cw laser beam is switched off by an acousto-optic switch (AOS) when the amplitude of the cavity output signal exceeds a predefined threshold and the subsequent temporal decay of the cavity output immediately after switching off the beam is recorded to determine the decay time and the cavity loss. This technique greatly improves the efficiency of the decay time measurement. However, it is costly and complicated because of the use of PZT and AOS.
Another cavity ring-down technique is developed for absorption spectroscopy by K. J. Schulz, W. R. Simpson in “Frequency-matched cavity ring-down spectroscopy”, Chem. Phys. Lett., Vol. 297, pp. 523, 1998. In this technique, the coupling of narrow-bandwidth laser power into a fixed-length cavity is obtained through laser frequency modulation. An external cavity diode laser (ECDL) provides a tunable laser beam, whose frequency is modulated back and forth across one of the longitudinal modes of the ring-down cavity. When the amplitude of the ring-down cavity output signal exceeds a pre-set threshold value, the incident laser beam is switched off and a ring-down signal is recorded to determine the total losses of the ring-down cavity. An acousto-optic modulator (AOM) is used to switch off the incident laser beam. The use of ECDL and AOM increases the complication of the apparatus.
A more complicated cavity ring-down technique is provided by I. Debecker, A. K. Mohamed, D. Romanini in “High-speed cavity ringdown spectroscopy with increased spectral resolution by simultaneous laser and cavity tuning”, Opt. Express, Vol. 13, No. 8, pp. 2906, 2005. They employ a fast tuning of the laser frequency, along with a rapidly swept ring-down cavity, to obtain cavity output signals with a high signal-to-noise ratio and also to improve the speed of absorption spectrum measurement. An optical isolator is also used for eliminating the effect of optical feedback from the ring-down cavity into the ECDL. Although a fast optical switch is not needed, their experimental apparatus, including a tunable ECDL and a PZT, is rather complicated.